Ushtrimi 6

Paraqitni më thjesht shprehjet:

a) $\cos 2x\cos x + \sin 2x\sin x$

b) $\sin 3x\cos 2x + \sin 2x\cos 3x$

c) $\sin \frac{x}{2}\cos x - \cos \frac{x}{2}\sin x$

d) $\cos x \cos 3x - \sin x \sin 3x$

e) $(\sin x + \cos x)^{2} + (\sin x - \cos x)^{2}$

f) $(\sin x - \cos x)^{2} + \sin 2x$

g) $(\operatorname{tg} x + \cot g x)(1 + \cos x)(1 - \cos x)$

h) $\frac{1 + \sin 2x}{(\sin x + \cos x)^{2}}$

i) $\frac{\operatorname{tg} x}{1 - \operatorname{tg}^{2} x} \cdot \frac{\cot g^{2} x - 1}{\cot g x}$